Problem StatementThe area under a curve can be estimated by breaking the x axis into increments, evaluating the function at a point inside that increment, and approximating the area under the curve in that increment as arectangle. The figure below shows this approximation with an increment of 1 and the function being evaluated at the midpoint of the increment.2018161412> 108640.511.52.533.54XAs the increment decreases, the approximation of the area under the curve improves as shown when the increments are decreased to 0.25 for the same function as shown above.2018161412> 108640.511.522.53.54Write the code that will calculate the area under the curve:y = 8 sin (x) + 0.5x² – x(where x is in radians)using decreasing increments until the area value converges (the difference between the area from two consecutive runs is less than 0.01%). Use the midpoint approximation method and start with an incrementof 1. Decrease the increment by half every iteration.Variable List% InputsUTF-8scriptLn 37Col 5 InputsThis section is only needed when running the code in MATLAB. MATLAB Grader automatically creates these variables.% Test Case 1Xmin11Xmax = 10;12% Test case output:13% area = 131.38231415% % Test Case 216% Xmin = 5;% Xmax% % Test case output:1710;1819% % area117.31782021% % Test Case 322% Xmin = 0;% Xmax100;% % Test case output:% % area = 161667 (1.6167e+05)242526Program27% Start writing your program here29UTF-8scriptO OH N345 6700 9 O1 ~34LO 6N N N NNN N N

Following is the Matlab code to find the area of the above function: clc; close all; %Taking all…

Problem Statement The area under a curve can be estimated by breaking the x axis into increments, evaluating the function at a point inside that increment, and approximating the area under the curve in that increment as a rectangle. The figure below shows this approximation with an increment of 1 and the function being evaluated at the midpoint of the increment. 25 35 As the increment decreases, the approximation of the area under the curve improves as shown when the increments are decreased to 0.25 for the same function as shown above. Write the code that will calculate the area under the curve: y = 8 sin (x) + 0.5x² – x (where x is in radians)

Problem Statement The area under a curve can be estimated by breaking the x axis into increments, evaluating the function at a point inside that increment, and approximating the area under the curve in that increment as a rectangle. The figure below shows this approximation with an increment of 1 and the function being evaluated at the midpoint of the increment. 25 35 As the increment decreases, the approximation of the area under the curve improves as shown when the increments are decreased to 0.25 for the same function as shown above. Write the code that will calculate the area under the curve: y = 8 sin (x) + 0.5x² – x (where x is in radians)

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question

Problem Statement
The area under a curve can be estimated by breaking the x axis into increments, evaluating the function at a point inside that increment, and approximating the area under the curve in that increment as a
rectangle. The figure below shows this approximation with an increment of 1 and the function being evaluated at the midpoint of the increment.
20
18
16
14
12
> 10
8
6
4
0.5
1
1.5
2.5
3
3.5
4
X
As the increment decreases, the approximation of the area under the curve improves as shown when the increments are decreased to 0.25 for the same function as shown above.
20
18
16
14
12
> 10
8
6
4
0.5
1
1.5
2
2.5
3.5
4
Write the code that will calculate the area under the curve:
y = 8 sin (x) + 0.5x² – x
(where x is in radians)
using decreasing increments until the area value converges (the difference between the area from two consecutive runs is less than 0.01%). Use the midpoint approximation method and start with an increment
of 1. Decrease the increment by half every iteration.
Variable List
% Inputs
UTF-8
script
Ln 37
Col 5

Inputs
This section is only needed when running the code in MATLAB. MATLAB Grader automatically creates these variables.
% Test Case 1
Xmin
11
Xmax = 10;
12
% Test case output:
13
% area = 131.3823
14
15
% % Test Case 2
16
% Xmin = 5;
% Xmax
% % Test case output:
17
10;
18
19
% % area
117.3178
20
21
% % Test Case 3
22
% Xmin = 0;
% Xmax
100;
% % Test case output:
% % area = 161667 (1.6167e+05)
24
25
26
Program
27
% Start writing your program here
29
UTF-8
script
O OH N345 6700 9 O1 ~34LO 6
N N N NN
N N N

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